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Suggested topics for a math DRP

Below is a list of suggested areas for your DRP reading:

  • Algebraic Geometry
  • Analysis_Harmonic
  • Analysis_Geometric
  • Analysis_PDE
  • Applied Math_Physical Math
  • Applied Math_Numerical Analysis
  • Category theory
  • Computer Science
  • Combinatorics
  • Differential Geometry
  • Game Theory
  • Geometry & Topology
  • Logic
  • Number Theory_Algebraic
  • Number Theory_Analytic
  • Machine learning
  • Probability
  • Representation Theory_Lie Groups
  • Representation Theory_Combinatorial
  • Statistics
  • Topology_Algebraic
  • Topology_Geometric
  • Topology_Symplectic
  • Topology_Combinatorial

Once you choose an area, you may specify a topic of interest from this list (courtesy of the University of Chicago math department's DRP program). These are only suggestions, and you are welcome to come up with others!

  • algebra/combinatorics
  • algebra/number theory
  • algebraic curves
  • algebraic curves and riemann surfaces
  • algebraic geometry
  • algebraic graph theory
  • algebraic k-theory
  • algebraic number theory
  • algebraic topology
  • algorithms of algebra and number theory
  • analytic number theory
  • applied mathematics
  • bass-serre theory
  • categorical logic
  • category theory
  • combinatorial game theory
  • combinatorial topology
  • combinatorics
  • combinatorics/number theory
  • commutative algebra and algebraic geometry
  • compact lie groups
  • complex algebraic curves
  • complex algebraic geometry
  • complex analysis
  • complexity theory
  • computability and algorithmic information
  • diffential forms in algebraic topology
  • differential geometry
  • differential geometry and general relativity
  • elementary number theory
  • elliptic curves
  • elliptic curves and cryptography
  • ergodic theory in number theory
  • euler characteristic and gauss-bonnet theorem
  • existence and uniqueness for ordinary differential equations
  • first-order logic and model theory
  • flows on manifolds
  • fourier analysis
  • galois theory of differential equations
  • game theory
  • geometry and differential forms
  • geometry of surfaces
  • geometry/topology
  • graph colorings
  • gröbner bases
  • group theory
  • harmonic analysis
  • homological algebra
  • hyperbolic geometry
  • introduction to characteristic classes
  • introduction to logic
  • introduction to manifolds
  • introduction to probability
  • knot theory
  • lie groups
  • lie groups and geometry
  • linear algebra
  • linear differential equations
  • local class field theory via lubin-tate theory
  • manifolds and lie groups
  • mathematical physics
  • matrix groups
  • model theory
  • models of peano arithmetic
  • mordell's theorem
  • nonstandard analysis
  • number fields and class groups
  • number theory
  • number theory and combinatorics
  • optimization theory
  • p-adic analysis
  • partial differential equations
  • probability
  • representation theory
  • representation theory and quantum mechanics
  • riemann surfaces
  • riemann surfaces and elliptic curves
  • sheaves, complex analysis and gaga
  • special (co)limits and kan extensions
  • stochastic processes
  • the borsuk ulam theorem
  • the fundamental group
  • the prime number theorem
  • the spectral theorem
  • topoi and logic
  • topological genericity
  • topology from the differential viewpoint
  • topology/analysis
  • topos theory in physics
  • tropical geometry
  • van der waerden's theorem
  • visual introduction to complex analysis
  • young tableaux
  • young tableaux and representations of the symmetric group
  • zeta functions of number fields